a+b=1
a^2+b^2=7 -->a^4+b^4=31
ile wynosi a i b
Tegoroczna matura podstawowa?:)
Do odnalezienia a,b wystarczą dwa pierwsze rownania. Z pierwszego wyznaczam i wstawiam do drugiego: , . Wtedy: Wtedy:
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Tegoroczna matura podstawowa?:)
Do odnalezienia a,b wystarczą dwa pierwsze rownania. Z pierwszego wyznaczam
i wstawiam do drugiego:
![a^2+b^2=7\\ a^2+(1-a)^2=7\\ a^2+a^2-2a+1=7\\ 2a^2-2a-6=0 a^2+b^2=7\\ a^2+(1-a)^2=7\\ a^2+a^2-2a+1=7\\ 2a^2-2a-6=0](https://tex.z-dn.net/?f=a%5E2%2Bb%5E2%3D7%5C%5C+a%5E2%2B%281-a%29%5E2%3D7%5C%5C+a%5E2%2Ba%5E2-2a%2B1%3D7%5C%5C+2a%5E2-2a-6%3D0)
,
. Wtedy:
![a_1=\frac{2+2\sqrt{13}}{4}=\frac{1+\sqrt{13}}{2} a_1=\frac{2+2\sqrt{13}}{4}=\frac{1+\sqrt{13}}{2}](https://tex.z-dn.net/?f=a_1%3D%5Cfrac%7B2%2B2%5Csqrt%7B13%7D%7D%7B4%7D%3D%5Cfrac%7B1%2B%5Csqrt%7B13%7D%7D%7B2%7D)
![a_2=\frac{2-2\sqrt{13}}{4}=\frac{1-\sqrt{13}}{2} a_2=\frac{2-2\sqrt{13}}{4}=\frac{1-\sqrt{13}}{2}](https://tex.z-dn.net/?f=a_2%3D%5Cfrac%7B2-2%5Csqrt%7B13%7D%7D%7B4%7D%3D%5Cfrac%7B1-%5Csqrt%7B13%7D%7D%7B2%7D)
![b_1=1-a_1=1-\frac{1+\sqrt{13}}{2}=\frac{1-\sqrt{13}}{2} b_1=1-a_1=1-\frac{1+\sqrt{13}}{2}=\frac{1-\sqrt{13}}{2}](https://tex.z-dn.net/?f=b_1%3D1-a_1%3D1-%5Cfrac%7B1%2B%5Csqrt%7B13%7D%7D%7B2%7D%3D%5Cfrac%7B1-%5Csqrt%7B13%7D%7D%7B2%7D)
![b_2=1-a_2=1-\frac{1-\sqrt{13}}{2}=\frac{1+\sqrt{13}}{2} b_2=1-a_2=1-\frac{1-\sqrt{13}}{2}=\frac{1+\sqrt{13}}{2}](https://tex.z-dn.net/?f=b_2%3D1-a_2%3D1-%5Cfrac%7B1-%5Csqrt%7B13%7D%7D%7B2%7D%3D%5Cfrac%7B1%2B%5Csqrt%7B13%7D%7D%7B2%7D)
Wtedy: